How to set iTunes 11 in shuffle or repeat mode via applescript

Question

According to http://dougscripts.com/ setting shuffle and repeat modes via applescript is broken in iTunes 11.

According to this stackoverflow answer shuffle is now a

Answer 1

For iTunes 12, this works

tell application "System Events"  
    tell process "iTunes" to if exists then  
        click menu item "Albums" of menu "Shuffle" of menu item "Shuffle" of menu "Controls" of menu bar 1  
    end if  
end tell

Change Albums to Songs, Groupings, On and Off accordingly.